The reason people say that balancing a tank is more important than killing algae is simple. You don't have to kill algae.
Anything you buy in a bottle to kill algae is harmful to both your fish and your plants. It is especially harmful to shirmp, and they die, been there. Just because something doesn't kill your plants doesn't make not harmful.
I don't do Excel spot treatments anymore. I have melted enough plants to stop. I am willing to do H2O2 but it depends on what it is for. When I know what caused the algae (making adjustments, missing doesing, etc), I will use it as a quick fix to just get it out. If I don't know why it is there, I try to let it linger.
I have gassed my fish pretty bad too. I don't recall if I ever lost any, I probably have, but I defineatly made them suffer. I can admit that as well.
In general, when I started I made mistakes, for the sake of algae, that killed the animals (and sometimes plants) I was keeping. It's just not a good idea. Maybe you can get away with it if you are very methodical but with that approach, you are likely someone who is patient and can achieve a balance.
Anyway, more of my point is this. When I started, I was using everything under the sun to try to keep algae at bay. Not only was it a ton of work, my tank eventually just crashed. My next tank, it never crashed but it just was never in the state I wanted.
After that, I really challenged myself to do non CO2 tanks. Not necessarily low light, defineatly not "low light plants". I used stems that are said to need CO2, massive amounts of ferts, and crazy amount of light. I successfully kept 3 tanks without a major algae outbreak. In fact, the little ones I got were always from an experimental perspective.
I would add light and see how much I could use before something bad would happen. I don't think I ever got more than some algae on the glass. I would reduce light (most were using screw in CFL bulbs so that was easy), and things would go back.
I unintentionally learned that lighting can control every other factor. Before, I was trying to use CO2, ferts, and anything else to control both growth and algae, while having too much light. I did have a long run with 108 watts of T5 lighting over a 29 but it crashed. My non CO2 ones never change.
Now I am learning to apply this to high tech tanks. It's a much more delicate balance (IMO). But, the same rules apply. Honestly, one great thing is that we have so much information on algae. I have found that algae is a "telling sign". I now am able to understand by research what I lack in my tank and make adjustments (one by one, never doing an "algae war"). I learn something each time I get algae and successfully get rid of it.
At the end of the day, I may use H2O2, but that is it. It's not to mask the problem, it's to save time. I do have one tank right now that isn't balanced, and I get more algae than I would like. I am playing a game though. I am seeing if I can get away by adding plants. I have put a screen under the light and in 3-4 days, my algae was cut down so significantly, it was shocking to me. I don't mind experimenting, but I like to know my "way out", not constantly working towards an unachievable goal.